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13.Oscillations
normal
A steady force of $120\ N$ is required to push a boat of mass $700\ kg$ through water at a constant speed of $1\ m/s$ . If the boat is fastened by a spring and held at $2\ m$ from the equilibrium position by a force of $450\ N$ , find the angular frequency of damped $SHM$ ..... $rad/s$
A
$0.56$
B
$0.21$
C
$1.35$
D
Motion is overdamped
Solution
$\mathrm{b}=\frac{\mathrm{F}}{\mathrm{v}}=\frac{120}{1}, \mathrm{r}=\frac{\mathrm{b}}{2 \mathrm{m}}=\frac{60}{7000 \times 2}$
$\omega=\sqrt{\omega_{0}^{2}-r^{2}}$
$\mathrm{kx}=\mathrm{F}$
$\mathrm{k}=\frac{450}{2}=225=\sqrt{\frac{225}{700}-\frac{60^{2}}{700^{2}}}$
$=\sqrt{\frac{225 \times 700-3600}{700^{2}}}=0.56 \mathrm{rad} / \mathrm{s}$
Standard 11
Physics
